You know the signs of the factors must be a plus and a minus, so ( + ) ( - ) the two on your x squared lets you know that you need a two x. And the 1 tells you both end digits must be 1. (2x-1) (x +1) is the only combination that works to leave you with one quantity of positive x.

Here's an outline of the solution: As pointed out by Student100 the substitution ##\cos\theta\leadsto x## produces a quadratic, and if you know the roots of a quadratic -- say ##ax^2+bx+c## with roots ##r_1,r_2## if any -- then you can factor it as ##a(x-r_1)(x-r_2)##. The only step that remains is to “undo” the substitution by replacing ##x## with the original ##\cos\theta##. I hope you can achieve all of those steps to find your desired answer. ;-)